Pointwise uniformly rotund norms

On non-midpoint locally uniformly rotund normability in Banach spaces

We will show that if X is a tree-complete subspace of ∞ , which contains c 0 , then it does not admit any weakly midpoint locally uniformly convex renorming. It follows that such a space has no equivalent Kadec renorming. 1. Introduction. It is known that ∞ has an equivalent strictly convex renorming [2]; however, by a result due to Lindenstrauss, it cannot be equivalently renormed in locally u...

Rotund Norms, Clarke Subdifferentials and Extensions of Lipschitz Functions

A Constructive Analysis of Convex-Valued Demand Correspondence for Weakly Uniformly Rotund and Monotonic Preference

Bridges 1992 has constructively shown the existence of continuous demand function for consumers with continuous, uniformly rotund preference relations. We extend this result to the case of multivalued demand correspondence. We consider a weakly uniformly rotund and monotonic preference relation and will show the existence of convex-valued demand correspondence with closed graph for consumers wi...

Pointwise Domination of Matrices and Comparison of ^ Norms

when (1) holds. For one need only write out the trace explicitly in terms of matrix elements. In a more general context, we conjectured in [5] that (1) implies (3) whenever p ^ 2. The attractiveness of this conjecture is shown by the fact that I know of at least five people other than myself who have worked on proving it. It was thus quite surprising that Peller [3] announced that (3) fails for...

Locally Uniformly Convex Norms in Banach Spaces and Their Duals

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm that is itself locally uniformly convex.